The Bruins will face No. 2 seed Kentucky in the South Regional semifinals Friday in Memphis.
Cincinnati (30-6) had no real answer when the Bruins got rolling falling short of their first Sweet 16 appearance since 2012.
Jarron Cumberland had 15 points to lead the Bearcats.
This marquee matchup pitted the nation's highest-scoring team against one of the best defensive teams.
UCLA led the nation in scoring at 90.6 points per game and assists with 21.6 a game. The Bruins rolled to 97 points in their opening win against Kent State.
The Bearcats are ranked fifth nationally in scoring defense at 60.8 per game and 11th in adjusted defensive efficiency in KenPom.com's calculations.
Cincinnati showed off its offensive abilities in its opener, hitting a school NCAA Tournament-record 62 percent from the field, while UCLA continued its season-long struggles at the defensive end to allow Kent State to keep their first-round game close until late.
The Bearcats got the best of this clash of styles in the first half, holding the Bruins mostly in check while continuing their good shooting from the opener. Cincinnati hit 12 of 24 shots and led by six points, but UCLA showed some offensive life late in the half to pull within 33-30.
The Bruins found their groove to start the second half, getting out in transition and knocking down 3-pointers.
Ball hit two straight 3s, then Bryce Alford dropped in another. In a matter of seconds, UCLA was up 55-47.
The Bruins kept pushing and kept making shots, stretching the lead to 12. Cincinnati tried to make a late run, but UCLA kept making shots, hitting 19 of 30 in the second half.
Cincinnati's season ended with a thud, but the Bearcats finished with their second 30-win season as a program and were one short of the school record for victories.
UCLA can be an unstoppable force when it gets rolling on offense. The Bruins tightened up defensively in the second half as well, making them looking like a formidable threat to get through Memphis to the Final Four.
UCLA moves on to face No. 2 seed Kentucky in the South Regional semifinals Friday in Memphis.